Various methods and systems for sub-Nyquist signal processing are known in the art. For example, U.S. Pat. No. 8,457,579, whose disclosure is incorporated herein by reference, describes a method for signal processing that includes distributing an analog input signal to a plurality of processing channels. In each processing channel, the input signal is mixed with a respective periodic waveform including multiple spectral lines, so as to produce a respective baseband signal in which multiple spectral slices of the input signal are superimposed on one another. The baseband signal produced in each of the processing channels is digitized, to produce a set of digital sample sequences that represent the input signal.
U.S. Pat. No. 8,032,085, whose disclosure is incorporated herein by reference, describes a signal processing method that includes sampling an analog signal, which has a spectral density defining one or more bands, to produce a digitized signal. A spectral transform of the digitized signal is expressed as a matrix multiplied by a vector, wherein the vector includes multiple elements that represent the spectral density of the analog signal as a function of frequency within respective spectral slices. Indices of a subset of the elements of the vector, in which the spectral density is concentrated, is determined. The analog signal is reconstructed from the digitized signal using the subset of the elements of the vector and a corresponding subset of columns of the matrix having the indices.
U.S. Patent Application Publication 2011/0225218, whose disclosure is incorporated herein by reference, describes a method that includes accepting an analog input signal that includes a sequence of pulses. The analog input signal is filtered so as to produce a filter output, using a filter whose time-domain response is confined to a finite time period and whose frequency-domain response is non-zero at a finite set of integer multiples of a frequency shift Δω, and is zero at all other integer multiples of Δω. The filter output is sampled so as to produce digital samples. Respective amplitudes and time positions of the pulses in the sequence are calculated based on the digital samples.
U.S. Patent Application Publication 2013/0038479, whose disclosure is incorporated herein by reference, describes a method that includes accepting an analog input signal including a sequence of pulses of a given pulse shape. The analog input signal is distributed to multiple processing channels operating in parallel. The analog input signal is sampled by performing, in each of the multiple processing channels, the operations of: mixing the analog input signal with a different, respective modulating waveform to produce a mixed signal; filtering the mixed signal; and digitizing the filtered mixed signal to produce a respective digital channel output.
U.S. Patent Application Publication 2013/0187682, whose disclosure is incorporated herein by reference, describes a method for signal processing that includes accepting an analog signal, which consists of a sequence of pulses confined to a finite time interval. The analog signal is sampled at a sampling rate that is lower than a Nyquist rate of the analog signal and with samples taken at sample times that are independent of respective pulse shapes of the pulses and respective time positions of the pulses in the time interval.